Publications of the Astronomical Society of Australia

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1 Publishing Publications of the Astronomical Society of Australia Volume 18, 21 Astronomical Society of Australia 21 An international journal of astronomy and astrophysics For editorial enquiries and manuscripts, please contact: The Editor, PASA, ATNF, CSIRO, PO Box 76, Epping, NSW 171, Australia Telephone: Fax: Michelle.Storey@atnf.csiro.au For general enquiries and subscriptions, please contact: CSIRO Publishing PO Box 1139 (15 Oxford St) Collingwood, Vic. 366, Australia Telephone: Fax: pasa@publish.csiro.au Published by CSIRO Publishing for the Astronomical Society of Australia

2 Publ. Astron. Soc. Aust., 21, 18, 12 4 Australian Cosmic Ray Modulation Research M. L. Duldig Australian Antarctic Division, Channel Highway, Kingston, Tas. 75, Australia marc.duldig@utas.edu.au Received 2 August 31, accepted 2 October 5 Abstract: Australian research into variations of the cosmic ray flux arriving at the Earth has played a pivotal role for more than 5 years. The work has been largely led by the groups from the University of Tasmania and the Australian Antarctic Division, and has involved the operation of neutron monitors and muon telescopes from many sites. In this paper, the achievements of the Australian researchers are reviewed and future experiments are described. Particular highlights include: the determination of cosmic ray modulation parameters; the development of techniques for modelling ground-level enhancements; the confirmation of the Tail-In and Loss-Cone sidereal anisotropies; the Spaceship Earth collaboration; and the Solar Cycle latitude survey. Keywords: cosmic rays: observations modulation anisotropies neutron monitor muon telescope GLE: heliosphere 1 Introduction During the Second World War, the Physics Department of the University of Tasmania was heavily involved in the production of optical elements for Australia s defence effort. The Physics Department established the Optical Munitions Annexe, which grew to about 2 staff, producing roof prisms and photographic lenses. Toward the end of the war, it was recognised that there would be an influx of mature-age students to the University, and preparations were made to accommodate these returned servicemen. In 1945 A. G. (Geoff) Fenton was recalled from his position in charge of quality control at the Optical Munitions Annexe to the Physics Department to develop lecture and laboratory courses. He taught himself the necessary glassblowing and electronic techniques to build Geiger Müller counter tubes for laboratory experiments in nuclear physics involving radioactivity. This in turn led to an interest in cosmic rays, which make up the largest fraction of the natural background radiation. For an historical account of the period see A. G. Fenton (2) and references therein. From these beginnings a program of observation and discovery lasting over 5 years has grown. The research based in Tasmania has played, and continues to play, a significant role in our understanding of cosmic radiation. In the following sections we will look at some of the highlights of that research, with particular emphasis on more recent discoveries and plans to continue the legacy into the future. 2 The Early Years Much of the cosmic ray literature in the 193s discussed the east west effect that had been discovered with a two-tray Geiger Müller telescope (see Duldig 1994 for a description of cosmic ray telescopes). An asymmetry had been found in the response at the geomagnetic equator of 15% (total intensity) to 3% (hard component) at 45 zenith angle, with the maximum response arriving from the west and minimum from the east. This was correctly interpreted as arising because the majority of the cosmic rays were positively charged and probably protons (Johnson & Street 1933; Johnson, Barry & Schutt 194; Johnson 1941). Seidl (1941) had shown that there was a much smaller east west asymmetry at the higher magnetic latitude of 54 N at New York. His measurements indicated a statistically significant value somewhat smaller than 1%. Geoff Fenton saw this as a measurement that could be repeated from Hobart at a similar southern geomagnetic latitude of 52. Fenton and D. W. P. (Peter) Burbury constructed a two-tray Geiger Müller telescope on a turntable and with adjustable zenith angle of view. The results, which demonstrated that the southern hemisphere asymmetry was identical to that observed by Seidl in the north, were submitted to Physical Review for publication in April 1948 and were published in September of the same year (Fenton & Burbury 1948). This was the first cosmic ray research project of the group, and formed the basis of Peter Burbury s PhD studies (Burbury 1951). Peter Burbury later received the second PhD awarded by the University of Tasmania. 3 Establishing the Australian Network of Observatories 3.1 Surface Muon Telescopes In parallel with the development of the east west experiment in Hobart, the Physics Department at Melbourne University also began research in cosmic rays. The research team featured several notable names, including David Caro, Fred Jacka, John Prescott and Phil Law. A four-tray Geiger Müller telescope and an ionisation chamber were developed. This equipment made observations from Melbourne. Three further sets of equipment were constructed for deployment when the newly Astronomical Society of Australia /AS /1/112$5.

3 Australian Cosmic Ray Modulation Research 13 formed Australian National Antarctic Research Expedition (ANARE) bases were opened. In the summer of , one set of equipment was sent to each of Heard and Macquarie Islands and the final set was operated from HMAS Wyatt Earp. The testing and operation of the equipment and the Wyatt Earp voyage are described in Law (2). The results from the voyage were published in the year of the expedition (Caro, Law & Rathgeber 1948). In 1949 the equipment was returned from the islands for overhaul and maintenance, but in 195 the Melbourne group decided to discontinue cosmic ray research, putting its efforts into nuclear physics instead. Phil Law invited the Physics Department at the University of Tasmania to take over the ANARE work, and Geoff Fenton was put in charge. Early in 1949, the Hobart group was already building an east west telescope similar to the one above for deployment to Macquarie Island. This experiment was established on the island in 195 and operated alongside the Melbourne University experiment. A replacement telescope for the Melbourne University instrument was constructed at Hobart during 1951 and deployed the following summer. It continued operating until 3 March 1959, when fire destroyed the cosmic ray laboratory at Macquarie Island. Perhaps the most significant result from the instrument was the recording of the giant flare-induced ground-level enhancement (GLE) observed worldwide in February 1956 (Fenton et al. 1956). The east west telescope had been returned to Hobart at the end of A description of the Macquarie Island experiments and operations can be found in K. B. Fenton (2). N. R. (Nod) Parsons was appointed as the Australian Antarctic Division s officer in Hobart for the cosmic ray program following the changeover in responsibility for the research from Melbourne University to the University of Tasmania. Nod had been involved with the programs at both universities and had wintered at Macquarie Island with K. B. (Peter) Fenton in 195. The Mawson station was established on the Antarctic Continent in 1954 and a cosmic ray laboratory was added the following year. This housed a vertical telescope and an inclined telescope that could be set to any desired zenith angle and automatically rotated each hour to the next azimuth of a preset series. Nod Parsons was responsible for the installation and commissioning of the equipment and handed over a fine facility to R. M. (Bob) Jacklyn at the end of the year for the International Geophysical Year. Bob would later take over as head of the Australian Antarctic Division s research program. These telescopes and various upgraded replacements continued operating at Mawson until 1972, when a new laboratory that incorporated underground observations was constructed at the station. During August 1953, a vertical telescope was installed at the University campus in Hobart. A new cosmic ray observatory was constructed on the campus in 1975, and a new vertical telescope was run in parallel with the old one for some time. Continuous recording has continued to the present, giving almost 5 years of data. Ken McCracken installed a small 6 cm-square muon telescope at Lae at the same time as the neutron monitor was installed (see Section 3.3 below). In 1968, a new telescope system was added to the Mawson cosmic ray observatory. This consisted of two units viewing north and south at a zenith angle of 76,giving an effective atmospheric absorber depth of 4 metres water equivalent (mwe). This experiment would complement observations from the Cambridge underground telescopes (see Section 3.2 below), and results from the observations supported the case for an underground observatory at Mawson. A small vertical telescope was also operated at Macquarie Island in The new observatory at Mawson was constructed during 1971 and early 1972 as described below. The surface telescopes comprised three north and south highzenith-angle crossed systems using coincidences between vertical walls of Geiger Müller counters to view at the same zenith angle as the inclined system in the old observatory. The south-pointing telescope viewed across the geographic pole into the opposite temporal hemisphere as well as perpendicular to the local geomagnetic field. The result of such a view was to spread the rigiditydependent responses in time due to geomagnetic deflection (see Section below) of the incoming particles. The northern view reached equatorial latitudes which, in partnership with the underground system, gave complete southern hemisphere coverage from a single observing site (Jacklyn, Vrana & Cooke 1975). These surface counters were replaced by larger-area, multi-zenith angle proportional counter systems during 1986 and 1987 (Jacklyn & Duldig 1987; Duldig 199). 3.2 Underground Muon Telescopes One of the most important early developments was the decision by Geoff Fenton to operate underground telescopes in a disused railway tunnel at Cambridge near Hobart. The depth was shallow enough that the counting rate was still sufficiently high for useful studies and, perhaps more fortuitously, not so shallow that changes in atmospheric structure would have complicating effects on the telescope response. This latter feature was not known at the time. At the selected depth, studies of both solar and sidereal variations and their energy dependencies could be made. The instruments, based on those already put into operation at Mawson by Nod Parsons, commenced observations on 19 July 1957 (Fenton, Jacklyn & Taylor 1961). Planning for further underground telescopes was well under way in the early 197s. A deep underground system was installed in the Poatina power station in central Tasmania late in The depth of 357 mwe meant that the observations should be at energies beyond the influence of solar modulation, but the count rate was also low and several years of observation would be required to obtain significant results for the sidereal anisotropy (Fenton & Fenton 1972, 1975; Humble, Fenton & Fenton 1985; Jacklyn 1986).

4 14 M. L. Duldig Also during 1971, construction of the new Mawson surface/underground observatory was commenced (Jacklyn 2). Bob Jacklyn, who had assumed leadership of the Australian Antarctic Division s cosmic ray program, optimised the available telescope viewing directions to take advantage of both the geographic polar location and the position of the Mawson station relative to the magnetic pole. Telescopes were designed and constructed by Attila Vrana to put these plans into place. An 11 m vertical shaft was blasted into the granitic rock and two chambers were excavated at the bottom of the shaft. A surface laboratory was then constructed over the shaft. One underground chamber housed five cosmic ray telescopes. The remaining chamber was used for seismic observations. Three telescopes viewed north at a zenith angle of 24. This is aligned to the local magnetic field and the response is thus unaffected by any geomagnetic deflection of the arriving cosmic ray particles. Two smaller telescopes viewed southwest at 4 zenith angle. After accounting for geomagnetic bending (see Section below), the view of these telescopes is effectively along the Earth s rotation axis. They are therefore insensitive to the daily rotation of the Earth, viewing a fixed region over the south pole. Changes in their response do not arise from scanning an anisotropy but rather from isotropic variations in the cosmic ray density (i.e. changes in the total number of cosmic rays) near the Earth. Both the north and southwest telescope systems were subsequently upgraded to proportional counter systems in the early 198s (Jacklyn & Duldig 1983). 3.3 The Neutron Monitor Network During 1955, Ken McCracken began construction of Hobart s first neutron monitor as part of his PhD studies (McCracken 2). This monitor followed the Chicago design developed by John Simpson (Simpson, Fonger & Treiman 1953) that was later adopted as the standard neutron monitor for the International Geophysical Year (IGY). The counters thus became known as IGY counters, and installations of this type are described by the number of counters followed by the mnemonic (e.g. 12 IGY). Because the count rate of neutron monitors increases rapidly with altitude, the new instrument was sited at The Springs on Mt Wellington, 7 m above sea level. At the time this was the highest point on the mountain with good road access and electrical power. The counters employed BF 3 gas enriched in B 1. Cosmic ray neutrons interact with lead surrounding the counters, producing additional neutrons. These neutrons were further thermalised when passing through an inner paraffin moderator so that the cross section for neutron capture by the boron was optimal. Paraffin also surrounded the lead to act as a partial reflector redirecting some of the scattered neutrons back toward the counters. The neutron capture by boron produced an α-particle and a lithium ion, which were then detected by the proportional counter as a pulse, amplified and counted. B n Li7 3 + α For an extensive review of neutron monitor design see Hatton (1971). The monitor was installed at The Springs in July 1956, unfortunately after the giant GLE of February. As part of the IGY, several other monitors were also being constructed at this time. One was sent to Mawson and installed in early 1957, and another was installed at Lae, New Guinea, in April of the same year (McCracken 2). IGY counters were added to the network at Brisbane, Casey, Darwin, Wilkes and on the University campus in Hobart (Table 1). The Wilkes monitor was moved to Casey station with the rest of the Australian Antarctic operations in that region in The Mt Wellington monitor was destroyed by the major bushfires of 1967 around Hobart. An improved monitor design (Carmichael 1964), known as NM-64 or IQSY (International Year of the Quiet Sun) monitors, led to the eventual replacement of most IGY monitors worldwide. Installations of this type are also described by the number of counters followed by the mnemonic (e.g. 18 NM-64). The Darwin monitor was constructed using the new design in 1967, and the Mt Wellington monitor was similarly rebuilt in 197. Subsequently, Brisbane, Hobart and Mawson all upgraded to IQSY monitors. For a complete worldwide history of neutron monitor development, installation and use, readers should refer to the special issue of Space Science Reviews published recently (Bieber et al. 2). 3.4 Liaweenee Air Shower Experiment In the early 198s it was becoming clear that the sidereal daily variation at energies of ev had an amplitude of about.5% as measured by deep underground and small air shower experiments in the northern hemisphere. The only measurements in the southern hemisphere were from the Poatina power station telescopes at the bottom end of this energy window (Fenton & Fenton 1975; Humble, Fenton & Fenton 1985; Jacklyn 1986). A new air shower experiment was therefore installed in the central plateau region of Tasmania at Liawenee (Fenton et al. 1981, 1982; Murakami et al. 1984). This experiment showed that the southern hemisphere sidereal response was much smaller than that in the northern hemisphere at 2% (Fenton et al. 199), which was to have important implications for understanding the structure of sidereal anisotropies (see Section 7 below). 4 Recent Instrumentation 4.1 Hobart Surface Multi-directional Telescope In a collaboration between the Universities of Nagoya, Shinshu and Tasmania and the Australian Antarctic Division, a surface multi-directional scintillator telescope system was installed on the Sandy Bay campus of the University of Tasmania in December The telescope comprises two trays of 9 m 2 area (3 31m 2 scintillators) and generates 13 directions of view through appropriate coincidence circuitry (Fujii et al. 1994; Sakakibara et al. 1993). This experiment is located at approximately

5 Australian Cosmic Ray Modulation Research 15 Table 1. The Australian neutron monitor network Location Type Lat. Long. Alt. Cutoff From To Brisbane 12 IGY s.l. 7 2 GV 3 Nov Dec NM s.l. 7 2 GV 1 Jan 1977 Jun NM s.l. 7 2 GV 1 Jul Jan 2 Casey 12 IGY s.l. 1 GV 12 Apr Dec 197 Darwin 9 NM s.l. 14 GV 1 Sep 1967 Oct 2 Hobart 12 IGY m 1 88 GV 1 Mar Nov IGY m 1 88 GV 1 Nov NM m 1 88 GV 1 Apr 1978 Kingston 9 NM m 1 88 GV 2 Apr 2 Nov 2 18 NM m 1 88 GV Nov 2 Lae 3 IGY s.l GV 1 Jul Feb 1966 Mawson 12 IGY m 22 GV 1 Apr Oct IGY m 22 GV 1 Jan Feb NM m 22 GV 13 Feb 1986 Mt Wellington 12 IGY m 1 89 GV Jul Jan NM m 1 89 GV 5 Jun 197 Transportable 3 NM-64 Tasmania and Delaware Universities and the Australian Antarctic Division are presently using this instrument for annual shipborne latitude surveys between Seattle and McMurdo Wilkes 12 IGY s.l. 1 GV 5 Mar Apr 1969 the co-latitude of the Nagoya surface telescope system, and results in almost complete latitude coverage of both hemispheres. The bi-hemisphere collaboration was established to study solar and sidereal anisotropies and Forbush decreases. These decreases are associated with geomagnetic storms, and the telescope system has been used to identify precursor cosmic ray signatures (see Section 8 below). 4.2 Liapootah Underground Multi-directional Telescope The same collaboration that established the Hobart surface telescope system also installed an underground multidirectional telescope in an access tunnel at the Liapootah power station in central Tasmania (Mori et al. 1991, 1992; Humble et al. 1992). The major thrust of research for this telescope system is the study of sidereal anisotropies, and it has played a key role in deducing the structure of these anisotropies (see Section 7 below). 4.3 Transportable Neutron Monitor The University of Tasmania and the Australian Antarctic Division jointly developed a transportable neutron monitor to undertake a cosmic ray latitude survey in early 1991, around the time of the last solar maximum (Humble et al. 1991a). The equipment is housed in an insulated 2 foot shipping container and consists of a slightly modified 3 NM-64 monitor. The container was carried aboard the Australian research and supply icebreaker Aurora Australis from Hobart to Mawson in January 1991, where it was offloaded for two months before returning in March. A second survey from Hobart to Mawson and return was conducted over the summer of (Humble et al. 1991a). A new collaborative program with the Bartol Research Institute of the University of Delaware began in 1994, when the monitor was loaded onto the US Coast Guard icebreaker Polar Star in Hobart. The monitor then surveyed from Hobart to McMurdo and on to Seattle (Bieber et al. 1995). When it arrived in the USA, the Bartol group added inclinometers so that the response of the monitor could be more accurately determined (Bieber et al. 1997). The monitor has since undertaken annual latitude surveys between Seattle and McMurdo, and will do so for at least a full solar cycle. During the survey, a new He 3 counter was employed in place of one of the BF 3 counters (Pyle et al. 1999). The aim of this exercise was to demonstrate that new and cheaper counters could be used as replacements for the ageing IQSY counters while maintaining almost identical response characteristics. 4.4 Kingston Neutron Monitor The Brisbane neutron monitor was decommissioned at the end of January 2 and transported back to Hobart. The monitor was then installed in a new observatory at the Kingston headquarters site of the Australian Antarctic Division. In October 2, the Darwin monitor will be similarly moved to the Kingston observatory, resulting in an 18 NM-64 monitor with high counting rate. This monitor and a similar one at Mawson will continue observations for the foreseeable future. 5 Cosmic Ray Modulation 5.1 The Heliosphere The heliosphere is the region of space where the solar wind s momentum is sufficiently high that it excludes the interstellar medium. This region is thus dominated

6 16 M. L. Duldig Intersetellar Medium Heliopause Astronomical Unit Expanding Solar Wind Sun Heliosphere Shock Front Heliosheath Possible Bow Shock Magnetic Field Lines Interstellar Medium Figure ) Schematic view of the heliosphere and its interaction with the interstellar medium. (From Venkatesan & Badruddin by the solar magnetic field carried outward by the solar wind plasma. Galactic cosmic rays beyond this region are considered to be temporally and spatially isotropic, at least over timescales of decades to centuries. It is likely that the heliosphere is not spherical but that it interacts with the interstellar medium as shown schematically in Figure 1. Cosmic rays enter the heliosphere due to random motions, and diffuse inward toward the Sun, gyrating around the interplanetary magnetic field (IMF) and scattering at irregularities in the field. They will also experience gradient and curvature drifts (Isenberg & Jokipii 1979) and will be convected back toward the boundary by the solar wind and lose energy through adiabatic cooling, although the latter process is only important below a few GeV and does not affect ground-based observations. The combined effect of these processes is the modulation of the cosmic ray distribution in the heliosphere (Forman & Gleeson 1975). It should be remembered that the approximately 11-year solar activity cycle is reflected in the strength of the IMF, the frequency of coronal mass ejections (CMEs) and shocks propagating outward, and the strength of those shocks. The solar magnetic field reverses at each solar activity maximum, resulting in 22-year cycles as well. The field orientation is known as its polarity and is positive when the field is outward from the Sun in the northern hemisphere (e.g. during the 197s and 199s) and negative when the field is outward in the southern hemisphere. A positive polarity field is denoted by A> and a negative field by A<. 5.2 Heliospheric Neutral Sheet The expanding solar wind plasma carries with it the IMF. A neutral sheet separates the field into two distinct hemispheres, one above the sheet, with the field either emerging from or returning to the Sun, and the other below the sheet, with the field in the opposite sense. The solar magnetic field is not aligned with the solar rotation axis and is also more complex than a simple dipole. As a result, the neutral sheet is not flat but wavy, rotating with the Sun every 27 days. At solar minimum, the waviness of the sheet is limited to about 1 helio-latitude but near solar maximum the extent of the sheet may almost reach the poles. Figure 2 shows an artist s impression of the structure of the neutral sheet for relatively quiet solar times. With the rotation of the sheet every 27 days, the Earth is alternately above and below the sheet and thus in an alternating regime of magnetic field directed toward or away from the Sun (but at an angle of 45 to the west of the Sun Earth line). This alternating field orientation at the Earth s orbit is known as the IMF sector structure. The neutral sheet structure is such that there are usually two or four crossings per solar rotation. The example in Figure 2 is for a four-sector IMF. 5.3 Cosmic Ray Transport Early work by Parker (1965) and Gleeson & Axford (1967) paved the way for the theoretical formalism developed by Forman & Gleeson (1975) that describes the cosmic ray density distribution throughout the heliosphere. Isenberg & Jokipii (1979) further developed the treatment of the distribution function. Here we briefly summarise the formalism, following Hall, Duldig & Humble (1996). Isenberg and Jokipii (1979) showed that if F(x, p, t) describes the distribution of particles such that p 2 F(x, p,t)d 3 x dp d

7 Australian Cosmic Ray Modulation Research 17 Figure 2 Artist s impression of the structure of the heliospheric neutral sheet. (Artist: Werner Heil, 1977; commissioning scientist: John M. Wilcox.) is the number of particles in a volume d 3 x and momentum range p to p + dp centred in the solid angle d, then U + S =, (1) t where U(x,p,t)= p 2 F(x, p,t)d, S is the streaming vector, κ S(x,p,t)= CUV κ( U) 1 + (ωτ) 2 ( U) ωτκ 1 + (ωτ) 2 ( U ˆB), (2) and ω is the gyro-frequency of the particle s orbit, τ the mean time between scattering, κ the diffusion coefficient (isotropic), C the Compton Getting coefficient (Compton & Getting 1935; Forman 197), ˆB is a unit vector in the direction of the IMF, r the radial direction in a heliocentric coordinate system, V the solar wind velocity, and U is the number density of cosmic ray particles. As already noted, adiabatic cooling is relatively unimportant at the energies observed by ground-based systems and so it has not been included in Equation (1). Equation (2) may be considered in several parts. The first term describes the convection of the cosmic ray particles away from the Sun by the solar wind. The second and third terms represent diffusion of the particles in the heliosphere parallel to and perpendicular to the IMF respectively. The last term describes the gradient and curvature drifts. Jokipii (1967, 1971) expressed equation (2) in terms of a diffusion tensor κ κ T S = CUV κ ( U), κ = κ T κ, (3) κ 4π where κ, κ are the parallel and perpendicular diffusion coefficients, and the off-diagonal elements κ T are related to gradient and curvature drifts (see equation (5) below; Isenberg & Jokipii 1979). Then U = (CUV κ U). (4) t Equation(4) is a time-dependent diffusion equation known as the transport equation. If we note that ( ) U D = (κ U) t = (κ S U)+ ( κ A )( U) = (κ S U)+ V D U, (5) where ( U/ t) D refers only to the non-convective terms in equation (4) and κ S and κ A refer to κ being split into symmetric and anti-symmetric tensors, we find that κ A is the drift velocity, V D, of a charged particle in a magnetic field with a gradient and curvature. Thus equation (4) explicitly represents the transport of cosmic rays in the heliosphere by convection, diffusion and drift. 5.4 Modulation Model Predictions The diffusion and convection components of equation (4) are independent of the solar polarity and will only vary with the solar activity cycle. Conversely, the drift components will have opposite effects in each activity cycle following the field reversals. Jokipii, Levy & Hubbard (1977) and Isenberg & Jokipii (1978) investigated the effects of this polarity dependence by numerically solving the transport equation. They showed that the cosmic rays would essentially enter the heliosphere along the helioequator and exit via the poles in the A< polarity state. In the A> polarity state the flow would be reversed,

8 18 M. L. Duldig A> Field out in North A< Field out in South Particle Transport Sun Sun Particle Transport Neutral sheet little effect Neutral sheet significant effect Figure 3 Global cosmic ray transport predicted by modern modulation models. (From Duldig 2.) Figure 4 indicated. Long-term Climax neutron monitor observations and smoothed sunspot numbers. Solar magnetic reversals for each pole are with particles entering over the poles and exiting along the equator. This is shown schematically in Figure 3 (Duldig 2). Kota (1979) and Jokipii & Thomas (1981) showed that the neutral sheet would play a more prominent role in the A< state when cosmic rays entered the heliosphere along the helio-equator and would interact with the sheet. Because particles enter over the poles in the A> state, they rarely encounter the neutral sheet on their inward journey, and the density is thus relatively unaffected by the neutral sheet in this state. It was clear from the models that there would be a radial gradient in the cosmic ray density, and that the gradient would vary with solar activity. Thus the cosmic ray density would exhibit the 11-year solar cycle variation, with maximum cosmic ray density at times of solar minimum and minimum cosmic ray density at times of solar maximum activity (and field reversal). Figure 4 shows this anticorrelation from the long record of the Climax neutron monitor (for the data source see edu/neutronmonitor/misc/neutron2.html). Jokipii & Kopriva (1979) extended the analysis and showed that the A< polarity would have larger radial gradients of particles. It is also apparent from Figure 4 that the cosmic ray peaks at solar minimum alternate from sharply peaked in the A< polarity state to flat-topped in the A> state. This is not well fitted by modulation models but is clearly related to the polarity differences and probably to the effects of the neutral sheet on the cosmic ray transport shown in Figure 3. Jokipii & Kopriva (1979) also found that the transport of cosmic rays would result in a minimum in the cosmic ray density at the neutral sheet during A> polarity states and a maximum at the neutral sheet in the A< state. There would therefore be a bi-directional latitudinal (or vertical) gradient, symmetrical about the neutral sheet and reversing in sign with each solar polarity reversal. Jokipii & Davila (1981) and Kota & Jokipii (1983) further developed the numerical solutions with more realistic models and more dimensions to the models. They found that the minimum density at the neutral sheet predicted for the A> state would be

9 Australian Cosmic Ray Modulation Research Heliographic Latitude Min Min Equator Heliographic Longitude Figure 5 The predicted latitudinal distribution of cosmic rays near the heliospheric neutral sheet in the A>polarity state. (From Kota & Jokipii 1983.) slightly offset from the neutral sheet, as shown in Figure 5 (Jokipii & Kota 1983). Independently, Potgieter & Moraal (1985) made the same predictions, using a model with a single set of diffusion coefficients. More recent models have included polar fields that are less radial than previously thought, but the predictions of the models remain generally the same (Jokipii & Kota 1989; Jokipii 1989; Moraal 199; Potgieter & Le Roux 1992). It is worth noting that the Ulysses spacecraft found that the magnetic field at helio-latitudes up to 5 was well represented by the Parker spiral field, but that there was a large amount of variance in the transverse component of the IMF (Smith et al. 1995a,b). 5.5 Solar Diurnal Anisotropy Forman & Gleeson (1975) showed that the cosmic ray particles would co-rotate with the IMF. At 1AU this represents a speed of order 4 km s 1 in the same direction as the Earth s orbital motion (at 3 km s 1 ). Thus the cosmic rays will overtake the Earth from the direction of 18 hours local time, as shown in Figure 6. Drift terms were neglected by Forman & Gleeson (1975), and their results indicated that the anisotropy should have an amplitude of 6%. Later models by Levy (1976) and Erdös & Kota (1979) which included drifts showed that the anisotropy should have an amplitude given by 6 1 α 1 + α %, where α = κ /κ = λ /λ is ratio of perpendicular to parallel diffusion coefficients, which can be shown to be equal to the ratio of the perpendicular and parallel mean free paths of the particles. The arrival direction of the anisotropy is also affected by drifts, shifting from 18 hours local time in the A< polarity state to 15 hours local time in the A>state. In Figure 7 we see observations of the anisotropy from View From Above Ecliptic Plane Sun 12 LT 6 LT Earth 18 LT Earth's Orbit 3 km/s LT Corotational Streaming 4 km/s Figure 6 The solar diurnal anisotropy resulting from co-rotational streaming of particles past the Earth. This view from above the ecliptic plane shows local solar times. (From Hall et al. 1996; Duldig 2.) a number of underground telescopes. These observations are not corrected for geomagnetic bending, so the absolute phases do not generally represent those of the anisotropy in free space. The changes in phase of the anisotropy are, however, readily apparent at the times of solar field reversal. It should also be noted that the Mawson underground north telescope views along the local magnetic field and is not subject to geomagnetic deflections (see Section 3.2 above), and hence shows the expected free-space phases. Rao, McCracken & Venkatesan (1963) analysed the solar diurnal anisotropy, ξ SD, as observed by neutron monitors, and concluded that it arose from a streaming of particles from somewhere close to 9 east of the Sun Earth line (i.e. 18 hours). The spectrum was assumed to be a power law in rigidity ( ξ SD =ηp γ, where η is an amplitude constant, γ the spectral exponent and P is rigidity) with some cutoff to the rigidity of particles that were responsible for the anisotropy. This cutoff became known

10 2 M. L. Duldig.1% Hobart Vertical hr.1% Hobart North hr 18 hr hr 18 hr 6 hr hr 12 hr.1% Mawson Underground North hr 18 hr 6 hr hr Embudo North.1% hr 18 hr 6 hr 18 hr.1% Embudo Vertical hr 6 hr hr hr Figure 7 Underground observations of the solar diurnal variation uncorrected for geomagnetic bending. The change of phase after each IMF reversal can be clearly seen. The years of reversal are shown. It should be noted that the Mawson underground north telescope is unaffected by geomagnetic bending and shows the phases expected. Top left: Hobart vertical; top right: Hobart north; centre: Mawson north; bottom left: Embudo north; and bottom right: Embudo vertical. (From Duldig 2.) as the upper limiting rigidity (P u ) of ξ SD. Although P u is generally employed as a sharp spectral cutoff, it is in reality the rigidity at which the anisotropy ceases to contribute significantly to a telescope response. Rao et al. (1963) found that the anisotropy was independent of rigidity (γ = ) and P u was 2 GV. Further analysis by Jacklyn & Humble (1965) found that P u was not constant. This was confirmed by Peacock & Thambyahpillai (1967) and Peacock, Dutt & Thambyahpillai (1968), who showed P u varying from 13 GV during the period to 7 GV in Duggal, Pomerantz & Forbush (1967) showed that the amplitude was not constant. Jacklyn, Duggal & Pomerantz (1969) were able to show that these changes were not due to a change in the spectrum but that P u did vary in the manner described by Peacock et al. (1968) and that the amplitude also varied as described by Duggal et al. (1967). Furthermore, they showed that the spectral exponent was slightly negative (γ =.2). Ahluwalia & Erickson (1969) and Humble (1971) also found P u varied but did not agree about the spectral index, finding that it was and slightly positive respectively. Concurrently with these studies, Forbush (1967) showed that there was a 2 year cycle of variation in data recorded by ionisation chambers from 1937 to Duggal & Pomerantz (1975) subsequently verified conclusively that there is a 22-year variation in the anisotropy that is directly related to the solar polarity. Forbush (1967) had suggested that the long-term variation was due to two components. Duggal, Forbush & Pomerantz (1969) investigated the two components and determined that they had the same spectrum. Ahluwalia (1988a,b) disagreed that there were two independent components always present,

11 Australian Cosmic Ray Modulation Research 21 but conceded that there were two components during the A> polarity state, one radial and the other aligned in the east west (18 hours local time) direction, termed the E W anisotropy. He argued that the radial component disappeared during the A< polarity state. This could explain the 22-year phase variation in the anisotropy. Swinson, Regener & St John (199) showed that the radial component of the anisotropy was correlated with the square of the IMF magnitude, indicating that the radial component must be related to the convection of particles away from the Sun. This convection is generated by IMF irregularities carried radially outward by the solar wind. The correlation found by Swinson et al. (199) was greater during A> polarity states, in agreement with the results of Ahluwalia (1988a,b). Ahluwalia (1991) and Ahluwalia & Sabbah (1993) discovered a correlation between P u and the magnitude of the IMF. Unexpectedly high values of P u were observed after the solar maximum of 1979, increasing to 18 GV in These results were confirmed by Hall, Humble & Duldig (1993). The most recent analysis of the anisotropy was carried out by Hall (1995) and Hall, Duldig & Humble (1997). These results are reproduced in Figure 8 and are derived from a study using seven neutron monitors, four underground telescopes and one surface telescope, covering a rigidity range of GV from 1957 to 199. The 11-year variation in the amplitude is clear and there is some evidence for an 11-year period in P u. The four very large values of P u are probably unreliable, as the χ 2 contours of the fit indicated a large range of possible solutions. The spectrum also appears to depend on the solar polarity, with the A> polarity state (197s) showing positive spectral indices for much of the time. SD (%) P u (GV) Best fit parameters of SD Figure 8 Solar diurnal variation, annual average best-fit parameters. Typical 1σ errors are shown. (From Hall et al ) Hall et al. (1997) summarised the results of the analysis of the anisotropy for the period They concluded that: 1. the anisotropy had a spectral index of 1 ± 2 and an upper limiting rigidity of 1 ± 25 GV; 2. the rigidity spectrum may be polarity-dependent; 3. the spectral index is relatively constant within a polarity state but the upper limiting rigidity varies roughly in phase with the solar cycle; and 4. the amplitude of the anisotropy varies with an 11-year solar-cycle variation that is not due to spectral variations. 5.6 North South Anisotropy Compton & Getting (1935) analysed ionisation chamber data for a sidereal variation and found that the peak of the variation had a phase of about 2 hours local sidereal time. The observations were all made in the northern hemisphere. Clearly an anisotropy existed, with a direction fixed relative to the background stars and not to the Sun Earth line as for the solar diurnal anisotropy. Subsequently, Elliot & Dolbear (1951) analysed southern hemisphere data and found a sidereal diurnal variation 12 hours out of phase from the result of Compton & Getting (1935). Jacklyn (1966) studied the sidereal diurnal variation in underground data collected at Cambridge in Tasmania. He employed two telescopes, one viewing north (into the northern heliospheric hemisphere) and the other vertically (into the southern heliospheric hemisphere). The southern view produced a maximum response at a phase of 6 hours local sidereal time, while the northern view gave a maximum response phase at 18 hours. Jacklyn (1966) attributed this to a bi-directional streaming (or pitch-angle anisotropy) along the local galactic magnetic field. Swinson (1969) disagreed, proposing instead that the anisotropy responsible for the sidereal diurnal variation was IMF sector polarity-dependent and directed perpendicular to the ecliptic plane. The streaming of particles perpendicular to the ecliptic had been described by Berkovitch (197), and Swinson realised that the anisotropy would have a component in the equatorial plane. Figure 9 shows how this north south anisotropy arises from the gyro-orbits of cosmic ray particles about the IMF. When the Earth is on one side of the neutral sheet (in one sector), there will be a component of the field parallel to the Earth s orbit, as shown in the top part of Figure 9. As the neutral sheet rotates, the Earth passes into the next solar sector and this component of the field reverses as in the bottom part of Figure 9. The direction of gyration of cosmic ray particles about the field reverses with the field reversal. Because a radial gradient is present, there is a higher density of cosmic rays farther from the Sun. Thus the region of higher density alternately feeds in from the south (top of Figure 9) and then the north (bottom of Figure 9). The region of lower particle density on the sunward side of the figure similarly reverses, giving rise to a lower flux at the opposite pole. The anisotropy

12 22 M. L. Duldig simply arises from a B G r flow, where G r represents the radial gradient of the particles. The flow of particles perpendicular to the helio-equator is not aligned with the Earth s rotation axis. Figure 1 shows the components of Ecliptic Plane Sun Sun Ecliptic Plane S S N Earth N Earth G r G r Interplanetary Field Interplanetary Field Figure 9 Schematic representation of the north south anisotropy and its dependence on the IMF direction. (From Duldig 2.) North-South Anisotropy Vector Earth x Sidereal Diurnal Variation Vector North-South Asymmetry Vector Heliographic Equator Figure 1 Geometric components of the north south anisotropy. (From Duldig 2.) the anisotropy as viewed from the Earth, and Figure 11 shows the geometry of the Earth s orbit, which must also be included in an analysis of the anisotropy. Nagashima et al. (1985) demonstrated that the solar semi-diurnal anisotropy (a pitch-angle or bi-directional anisotropy) is annually modulated, leading to a spurious sidereal variation that contaminates the real sidereal diurnal variation. In the case of the north south anisotropy this can be removed by appropriate analysis against the solar sectorisation and removal of the spurious response by the method of Nagashima et al. (1985). It turned out that both Jacklyn (1966) and Swinson (1969) were correct and that a bi-directional sidereal anisotropy and a sidereal anisotropy resulting from the north south anisotropy coexisted in the 195s and 196s. It would appear that the amplitude of the bidirectional anisotropy diminished greatly in the early 197s (Jacklyn & Duldig 1985; Jacklyn 1986) and has not recovered, a result that remains unexplained. There are several ways that the north south anisotropy may be derived from observations. The differences between northern- and southern-viewing telescopes at a single site, taking into account the expected responses, can be used. Similarly, the differences between the responses of northern and southern polar neutron monitors that have appropriate cones of view (see Section below) may be employed (Chen & Bieber 1993). Figure 12 shows the results of such an analysis by Bieber & Pomerantz (1986). Finally, analysis of the difference between the response to the sidereal diurnal anisotropy in the toward and away sectors of the IMF can be employed to derive the anisotropy (Hall 1995; Hall, Humble & Duldig 1994a; Hall, Duldig & Humble 1995a). A number of recent studies of the anisotropy have been undertaken by Australian researchers (Hall 1995; Hall et al. 1994a,b, 1995a,b). Figure 13 shows some of the results from these studies, which involved almost 2 detector-years of observation from 12 telescope systems at eight locations around the globe. 5.7 Deriving Modulation Parameters from Observations Yasue (198) and Hall et al. (1994a) have presented a complete description of the derivation of the anisotropy, ξ NS, Solar Rotation Axis Celestial Equator Sun 7.25 Ecliptic Plane Heliographic Equator Figure 11 Orientation of the Earth s rotation axis to the heliographic equator. (From Duldig 2.)

13 Australian Cosmic Ray Modulation Research NS (%) Year Figure 12 Derived amplitude of the north south anisotropy as determined from observations by northern and southern polar neutron monitors. (From Bieber & Pomerantz 1986). Deep River Neutron Monitor, hr hr 6 hr Mawson Surface Vertical Telescope, hr.1% hr 18 hr 6 hr.1% 12 hr Mawson U/G North Telescope, Hobart U/G Telescope, hr hr % 18 hr 6 hr 12 hr hr 6 hr % 12 hr Figure 13 Observed annual average toward away sidereal diurnal vectors from a sample of stations. The circles represent 1σ errors for individual years. (From Duldig 2; Hall 1995; Hall et al. 1994a,b, 1995a,b.) the rigidity spectrum and, as a result, the radial density gradient from multiple telescope and neutron monitor measurements of the sidereal variation. Assuming that there is little anisotropy arising from perpendicular diffusion compared with that caused by drifts, they showed that the radial density gradient as a function of rigidity, G r (P), is G r (P) A ξt NS (P) ρ sin χ, (6) where ρ is the gyro-radius of a particle at rigidity P and χ is the angle of the IMF to the Sun Earth line (typically 45 ). ξns T A (P) is a measurement of half the difference between ξ NS, averaged over periods when the Earth is in toward IMF sectors and when the Earth is in away IMF sectors. Thus it is possible to obtain a measure of the radial gradient at 1 AU directly from measurements of the sector-dependent sidereal diurnal variation. In a benchmark paper, Bieber & Chen (1991) further developed the cosmic ray modulation theory and showed that λ G r = 1 [ ASD cos χ δa 1 G(P) cos ( χ + t SD + δt 1 ) 1 1 ] + η ODV sin χ + η c cos χ, (7) where A SD and t SD are the annual average amplitude and phase of the solar diurnal anisotropy (ξ SD ), δa 1 1 and δt1 1 are the coupling coefficients that correct the amplitude and phase respectively to the free-space values of the anisotropy beyond the effect of the Earth s magnetic field (Yasue et al. 1982; Fujimoto et al. 1984), G(P) is the rigidity spectrum of the anisotropy, η ODV (=.45%) is the orbital Doppler effect arising from the motion of the Earth around its orbit, η c is the Compton Getting effect arising from the convection of cosmic rays by the solar wind, and χ is the angle of the IMF at the Earth. Forman (197) showed that η c = 1.5, assuming a solar wind speed of 4 km s 1, while Chen & Bieber (1993) used in situ solar wind measurements and found that there was no significant difference from the Forman (197) approximation.

14 24 M. L. Duldig The parameters A SD and t SD are derived directly from observations, while the spectrum can be deduced from observations by a number of telescopes with differing median rigidities of response. The remaining parameters may be considered constants. It is therefore possible to determine the average annual product of the radial gradient, G r, and the parallel mean free path, λ. Figures 14 and 15 show determinations of the product for neutron monitors and muon telescopes respectively. Bieber & Chen (1991) also showed that G z = sgn(i) [ αλ G r sin χ A SD ρ δa 1 G(P) sin ( χ + t SD + δt 1 ) 1 1 ] + η ODV cos χ η c cos χ, (8) where sgn(i) = { +1, A > IMF polarity state 1, A < IMF polarity state All the parameters are directly measured or known except α(= λ /λ ). The correct value of α has been strongly debated in the literature. Palmer (1982) estimated consensus values of the mean free paths from earlier studies. From his conclusions, α ranged between about 8 at 1 GV and 2 at 4 GV. Ip et al. (1978) derived a value of 26 ± 8 at 3 GV and Ahluwalia & Sabbah (1993) estimated that it must be < 9. Bieber & Chen (1991) assumed a value of.1 for their study. Hall et al. (1995b) studied the effect of varying α on derived modulation parameters. They found that the results were relatively insensitive to values of α between 1 and 1. They also derived upper limits to the value of α at various rigidities for both polarity states. In the A< state, the upper limit was 3 for rigidities between 17 GV and 185 GV. In the A> state, the situation was quite different, with an upper limit of about 15 at 17 GV and increasing with rigidity to very high values (> 8) at 185 GV. There appeared to be a strong dependence of the maximum value on the rigidity, although this does not guarantee that the actual value is similarly dependent. It would appear that a general consensus would be a value of 1 for neutron monitors, but that higher rigidity values require further study Separating G r and λ In the previous section we saw how the radial gradient, G r, and the average product of the radial gradient and the parallel mean free path, G r λ, could be independently determined from observations of the north south anisotropy and the solar diurnal anisotropy respectively. If we assume that G r λ = G r λ, then we are able to separate out the parallel mean free paths of cosmic rays near 1 AU, using equations (6) and (7). Chen & Bieber (1993) extended their formalism to show that G r = ξ NS ± ξns 2 + 4α tan ξ (ξ α tan χξ ). (9) 2ρ sin χ Figure 14 Three-year running average of λ G r for selected neutron monitor observations. Vertical lines indicate years of solar minimum. (From Bieber & Chen 1991.) G r (%) Mawson Vertical Surface Muon Telescope Mawson U/G, 24 North Muon Telescope Hobart Vertical U/G Muon Telescope Hobart U/G, 43 North Muon Telescope Figure 15 λ G r derived from muon telescope observations for particles between 5 and 195 GV. (From Hall et al. 1994b.) Hall (1995) derived a different but equivalent form of the equation, G r = ξ NS ± ξns 2 + 4ρ sin χ sgn(i)α(g rλ )G z. 2ρ sin χ (1)